Ali, N. H., & Abed, M. M. (2023). Some applications of weak-multiplication modules in neutrosophic set environment. Advances in the Theory of Nonlinear Analysis and Its Application, 7(4), 47–53.
- ISSN: 2587-2648
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Nibras H. Ali, Majid M. Abed
Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Ramadi, Iraq.
Recently it has been proven that the multiplication module is a Weak-multiplication module (W −M M ). In this paper, we present some applications of W − M M in neutrosophy theory. n-refined neutrosophic module M denoted by Mn(I). We proved that Mn(I) is regular and C.P.module. Also, every n-refined neutrosophic finitely generated ideal is a principal ideal of n-refined the ring R (Rn(I)). We proved that if
Mn(I) is multiplication module over ring Rn(I) and Mn(I) is of type S2; then every f. generated An(I) of Mn(I) is n-refined multiplication module. Also, if Rn(I) is n-refined neutrosophic ring, so Rn(I) is principal ideal ring if and only if every n-refined neutrosophic multiplication module Mn(I) is of type S. Finally, several results and applications have been presented in this paper with some new definitions, examples, and other properties.
Keywords: Multiplication module; Weak-multiplication module; Neutrosophic ring; Neutrosophic module; Regular ring.
Ali, N. H., & Abed, M. M. (2023). Some applications of weak-multiplication modules in neutrosophic set environment. Advances in the Theory of Nonlinear Analysis and Its Application, 7(4), 47–53.